I've heard that many times but I'm not so sure. For starters, if the fees are high, I don't think it would be convenient for unbanked people to make day-to-day payments with Bitcoin, besides they won't be able to do it in many places and the LN is impractical if not relying on third party wallets. The unbanked do not have enough to save much, they live from day to day and for little savings I think Bitcoin is the same as a bit of gold.
Bitcoin transaction fee is not like fee in bank transfer which will have different fee tiers with bank transfer values. Banks charg you more when your bank transfer has higher value.
Bitcoin transaction fee is different and only depends on transaction size and fee rate. With same input, output, address type you will have same transaction size. With same fee rate, two transactions will have same transaction fee even they move either $100 or $1000 bitcoin equivalent.
I agree with you that fee for bank transfer and Bitcoin transaction are always big problems for small value transfer or transaction.